# Tag Info

Accepted

### What happens when N increases in N-point DFT

The length N of the DFT is the number of frequency points that will result in the DFT output. Zero padding will result in more frequency samples, however this does not increase frequency resolution, ...
• 38.3k

### How does zero-padding affect the magnitude of the DFT?

All effects you see have to do with windowing. Your signal can be seen as a truncated (i.e., rectangularly windowed) sinusoid. If $s[n]$ is your signal, and $w[n]$ is the window, the signal you ...
• 80.9k

### Why Zero Padding in the Center of the DFT Interpolates / Upsamples the Signal (Sinc Interpolation / DFT Interpolation / Periodic Interpolation)

What you are experiencing is technically called interpolation by DFT; i.e., interpolating a time-domain sequence $x[n]$ by properly zero filling the middle portion of it's DFT $X[k]$ (and taking the ...
• 27.1k

Advantages of zero padding: If length of your sequence doesn't correspond to the size that can be handled efficiently with FFT routine (usually powers of prime numbers) then you might want to add ...
• 10.7k
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### How Exactly Does MATLAB Zero Pad Signal?

Lets say you have a vector $x = {\left[ 1, 2, 3, 4 \right]}^{T}$. You want to have a look on its DFT transform then you apply DFT on it and have the 4 points DFT transform of the data. In MATLAB it ...
• 42.4k
Accepted

### Zero padding - High amplitude

I'd like to apply zero padding to it, for better frequency bin resolution. First of all, let's state it one more time that zero padding does not improve frequency resolution of DFT. It'll only ...
• 27.1k

### How to Zero Pad in Order to Perform Filtering in the Fourier (Frequency) Domain?

There are 2 things to take under consideration in order to apply 2D Convolution in Frequency Domain: Padding and Shifting the Filter in order to match the size of the image. See my answer to Applying ...
• 42.4k
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### Merits of "Zero-Phase" Zero Padding

This is just about obtaining a symmetric signal after zero-padding. Take a symmetric signal (w.r.t. to time index $n=0$) and append zeros. Due to the implicit periodicity of the time signal used as ...
• 80.9k

### How to Zero Pad in Order to Perform Filtering in the Fourier (Frequency) Domain?

The result of a convolution of a data vector of length M with a kernel of length G is of length M + G - 1. (the maximum length of the non-zero portion, even though the limits of integration is ...
• 34.1k
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### Why is my time domain interpolation via zero-padding in frequency domain wrong?

The answer above is correct. Just to clarify a bit further, using x = np.linspace(0,10,5) will produce 5 numbers from 0 to 10 inclusively ...

### Relation of zero-padding and frequency resolution

why do I get "better" frequency resolution in case of adding zero-padding to this signal. You do and you don't. Zero padding increases resolution by interpolating between existing data ...
• 33.8k
Accepted

### Why to pad zeros at the middle of sequence instead at the end of the sequence?

When working with the DFT and IFFT we can zero pad the signal, which serves to interpolate new samples in the other domain. We will often see this applied with padding at the end of the sequence or ...
• 38.3k
Accepted

### Zeropadding and amplitude scaling

The conventional definition of the DFT for a length $N$ signal (without zero-padding) is $$X[k]=\sum_{n=0}^{N-1}x[n]e^{-j2\pi nk/N}\tag{1}$$ So there is no scaling involved. Scaling is applied to ...
• 80.9k

### Why should I zero-pad a signal before taking the Fourier transform?

I did not see these mentioned in the prior good responses so I will add the following additional important reasons for zero padding: Radix-2 algorithms are more efficient so zero padding out to the ...
• 38.3k
Accepted

For a) you're correct. For b), $x_1$ is a length $2N$ signal, and its DFT is given by $$X_1[k]=\sum_{n=0}^{2N-1}x_1[n]e^{-j2\pi kn/2N}=\sum_{n=0}^{2N-1}x_1[n]e^{-j\pi kn/N}\tag{1}$$ With $x_1=x[n]+x[... • 80.9k 3 votes ### How to perform a time domain shift in the frequency domain without zero padding You must zero-pad, whether implementing the delay in the time domain or the frequency domain. (Consider this: by delaying, you are making the signal longer.) Implementing the delay with the FFT ... • 31 3 votes ### Does Zero Padding Work as Advertised? Zero-padding data for a longer FFT is equivalent to interpolation by a (periodic) Sinc kernel. Interpolation by a (periodic) Sinc kernel can reconstruct points between samples of a signal that was ... • 34.1k 3 votes ### remove zero padding effect crosscorrealation so let's say the length of your FFT is$N$. let's say that you fill half of the buffer with your signal and fill the other half with zeros. $$x[n] = 0 \quad \text{ for } \tfrac{N}2 \le n < N ... 3 votes Accepted ### Zero padding effect on a FFT of gaussian noise Think about both questions separately. First of all, the (I)FFT is just an implementation of the (I)DFT, so I'm going to generalize all this to the DFT. Does the zero-padded IDFT retain variance? ... • 26.9k 3 votes Accepted ### DFT of sum of sinusoids with random zeroed samples The math is well known; it is the convolution theorem for the DFT. In this specific case:$$DFT\left\{f[n]\cdot z[n]\right\} = DFT\left\{f[n]\right\} * DFT\left\{z[n]\right\}$$Where:$f[n]$... • 2,565 3 votes Accepted ### DFT zero-padding of signals starting before n=0 Use the second one Tony... It yields the correct implied phase relationship. • 27.1k 3 votes Accepted ### Why do the lengths of the sampled signals$x_1, \: x_2$have to be$\text{length}(x_1)+\text{length}(x_2)-1\$?

Multiplication in the frequency domain is equivalent to circular convolution in the time domain with a period of NFFT. If you don't zero pad them to at least ...
• 2,638
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### Does Zero padding cause noise in the high frequency region?

Is that correct? No. This zero padding just leads to interpolation with a (cyclic) sinc kernel. It affects all subcarriers the same (as you can see in your own DFT!). So, this has to be a problem ...
• 26.9k
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### FFT peak estimation: Zero-padding vs signal repetitioon

If you repeat your data, you will have discontinuities where the sequence ends meet. These will cause spurious peaks in your spectrum. You could apply a window to the data to taper it at the edges, ...
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The disadvantage is you end up doing a longer FFT with higher computational cost: more MACs, energy spent toggling ALU/FPU transistors, memory paging and cache miss penalties, resulting in greater ...
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### How can I increase image size by zero padding?

I suppose the array names are not descriptive of the contents and you have simply repurposed them. To zero-pad from 8x8 to 32x32: ...
• 12.5k

### How does zero-padding affect the magnitude of the DFT?

Zero-padding does not affect DFT magnitude of the original N-DFT Samples. Overall energy does increase in the longer DFT and that is because we have introduced non-zero samples in between N-point DFT. ...
• 2,586
Accepted

### What proportion of a padded FFT should be actual values

Be careful with this in thinking that you would increase your frequency resolution- you won't! Zero padding is very effective in iterpolating more samples between the samples you have, but it does not ...
• 38.3k